Inventory Control

Why it matters

Inventory control is essential for maintaining the balance between supply and demand, minimizing holding costs, and ensuring smooth production processes. Effective inventory management can lead to significant cost savings and improved customer satisfaction by reducing stockouts and excess inventory.

Key ideas

• Inventory Types: Raw materials, work-in-progress (WIP), and finished goods are the primary types of inventory in industrial settings.
• Inventory Costs: These include holding costs, ordering costs, and shortage costs. Holding costs are associated with storing inventory, ordering costs are incurred during replenishment, and shortage costs arise when demand cannot be met.
• Economic Order Quantity (EOQ): A fundamental model used to determine the optimal order quantity that minimizes total inventory costs.
• Reorder Point (ROP): The inventory level at which a new order should be placed to avoid stockouts.
• Safety Stock: Extra inventory held to mitigate the risk of stockouts due to demand variability or supply chain disruptions.
• ABC Analysis: A method of categorizing inventory into three classes (A, B, and C) based on their importance and value, helping prioritize management efforts.

Formulas

• Economic Order Quantity (EOQ): EOQ = sqrt((2 * D * S) / H)
  • D: Annual demand (units/year)
  • S: Ordering cost per order (currency/order)
  • H: Holding cost per unit per year (currency/unit/year)
• Reorder Point (ROP): ROP = d * L + safety stock
  • d: Average demand per period (units/period)
  • L: Lead time (periods)
• Safety Stock: Safety Stock = Z * σd * sqrt(L)
  • Z: Z-score corresponding to the desired service level
  • σd: Standard deviation of demand in one specified period (units)
  • L: Lead time (periods)

The basic EOQ assumptions are stable known demand, instantaneous replenishment, fixed order/holding costs, no quantity discounts and no planned shortages. The safety-stock expression uses independent equal-variance period demands and fixed lead time; correlated demand or variable lead time requires a different variance calculation. A 95% cycle service level is not the same as a 95% unit fill rate.

Worked example

Given:

• Annual demand (D) = 10,000 units over 50 operating weeks
• Ordering cost (S) = ₹500 per order
• Holding cost (H) = ₹2 per unit per year
• Average demand per period (d) = 200 units/week
• Lead time (L) = 2 weeks
• Standard deviation of demand (σd) = 30 units/week
• Desired cycle service level = 95% (Z = 1.645), with independent weekly demand, fixed two-week lead time and a normal approximation to lead-time demand

1. Calculate EOQ:

   • EOQ = sqrt((2 * D * S) / H)
   • EOQ = sqrt((2 * 10000 * 500) / 2)
   • EOQ = sqrt(5000000)
   • EOQ = 2236.07
   • EOQ = 2236 units

2. Calculate expected lead-time demand:

   • ROP = d * L
   • ROP = 200 * 2
   • ROP = 400 units

3. Calculate Safety Stock:

   • Safety Stock = Z * σd * sqrt(L)
   • Safety Stock = 1.645 * 30 * sqrt(2)
   • Safety Stock = 1.645 * 30 * 1.414
   • Safety Stock = 69.72
   • Safety Stock = 70 units when rounded upward.

4. Reorder point = 400 + 70 = 470 units of inventory position (on-hand plus on-order minus backorders).

Common mistakes

• Confusing the units of demand and lead time, leading to incorrect ROP calculations.
• Ignoring variability in demand when calculating safety stock, resulting in stockouts.
• Misapplying the EOQ formula by not considering all relevant costs.

For GATE ME

Questions on inventory control often involve calculating EOQ, ROP, and safety stock. Practice problems that require understanding the interplay between different inventory costs and the impact of demand variability on inventory levels.

Quick check

1. What is the primary goal of inventory control?
2. How does safety stock help in inventory management?
3. What does the EOQ model optimize?

Answers: 1. To balance supply and demand while minimizing costs. 2. It mitigates the risk of stockouts due to demand variability. 3. It optimizes the order quantity to minimize total inventory costs.